import numpy as np
import sympy
import matplotlib.pyplot as plt

x = np.linspace(-np.pi,np.pi)
lhs = np.e**(1j*x)
rhs = np.cos(x)+1j*np.sin(x)
print (sum(lhs==rhs)==len(x))

z = sympy.Symbol('z', real = True)
sympy.expand(sympy.E**(sympy.I*z), complex = True)

for p in np.e**(1j*x):
    plt.polar([0, np.angle(p)],[0, abs(p)], marker = 'o')
plt.show()